Question

A party is thrown where 25 tables are used. Each table either sits 4 people or 6 people. A total of 116 people can be sat at the tables.
a) If y represent the number of four person tables and s represents the number of six person tables, write a
system of equations that models this situation.

b) How many six person tables are there?​

Answer 1

Answer:

(a) 4 y + 6 s  = 116 represents the given situation.

(b)There are 8  six- person tables at the party.

Step-by-step explanation:

Here, the total number of tables = 25

Let y  :  Represent the number of four person tables.

     s   :  Represents the number of six person tables.

Total people seated at all tables  = 116

Now, the number of people seated at table of 4  =  y x 4  = 4 y

         the number of people seated at table of 6  =  s x 6  = 6 s

(a)  Total People Seated = People seated at  { 4- table +  6  table}

      ⇒ 116  = 4 y + 6 s

       Hence, 4 y + 6 s  = 116 represents the given situation.

(b) Total tables are 25.      ⇒ s + y = 25

    Hence, the givens system of equations are:

    4 y + 6 s  = 116  ........  (1)

    s + y = 25   ............  (2)

Solving the above system, we get, substitute y = 25 - s    in (1)

4 y + 6 s  = 116   ⇒ 4(25-s)  + 6s = 116

or, 100 - 4s + 6s  = 116

or. 2s = 16

or, s = 16 / 2  = 8   ⇒ s = 8

Hence, there are 8  six- person tables at the party.